Nonseparating Cycles in 4-Connected Graphs
نویسندگان
چکیده
We prove that given any fixed edge ra in a 4-connected graph G, there exists a cycle C through ra such that G − (V (C) − {r}) is 2-connected. This will provide the first step in a decomposition for 4-connected graphs. We also prove that for any given edge e in a 5-connected graph G there exists an induced cycle C through e in G such that G−V (C) is 2-connected. This provides evidence for a conjecture of Lovász. Partially supported by NSF grant DMS 9970527
منابع مشابه
Shortest Co-cycle Bases of Graphs
In this paper we investigate the structure of the shortest co-cycle base(or SCB in short) of connected graphs, which are related with map geometries, i.e., Smarandache 2dimensional manifolds. By using a Hall type theorem for base transformation, we show that the shortest co-cycle bases have the same structure (there is a 1-1 correspondence between two shortest co-cycle bases such that the corre...
متن کاملA 9k Kernel for Nonseparating Independent Set in Planar Graphs
We study kernelization (a kind of efficient preprocessing) for NP-hard problems on planar graphs. Our main result is a kernel of size at most 9k vertices for the Planar Maximum Nonseparating Independent Set problem. A direct consequence of this result is that Planar Connected Vertex Cover has no kernel with at most (9/8 − ǫ)k vertices, for any ǫ > 0, assuming P 6= NP. We also show a very simple...
متن کاملGenerating cycles in graphs with at most one end
question of Halin, we prove that in a 3-connected graph wit nd the cycle space is generated by induced nonseparating iley Periodicals, Inc. J Graph Theory 00: 1–8, 2003
متن کامل0n removable cycles in graphs and digraphs
In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...
متن کاملVertex Removable Cycles of Graphs and Digraphs
In this paper we defined the vertex removable cycle in respect of the following, if $F$ is a class of graphs(digraphs) satisfying certain property, $G in F $, the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $. The vertex removable cycles of eulerian graphs are studied. We also characterize the edge removable cycles of regular graphs(digraphs).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 16 شماره
صفحات -
تاریخ انتشار 2003